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Seppo Linnainmaa (Pori (Finlandia), 1945) … Seppo Linnainmaa (Pori (Finlandia), 1945) è un matematico e informatico finlandese.Nel 1974 fu il primo a ricevere un dottorato in informatica dall'Università di Helsinki, e nel 1976 divenne assistant professor. Dal 1984 al 1985 fu visiting professor all'Università del Maryland e dal 1986 al 1989 fu presidente della Finnish Artificial Intelligence Society. Dal 1989 al 2007, anno del suo pensionameto, fu professore di ricerca al Technical Research Centre of Finland. Nel 1970 Linnainmaa introdusse nella sua tesi di M.Sc. la differenziazione automatica tramite accumulazione inversa, per calcolare efficientemente le derivate di una funzione differenziabile, applicando ricorsivamente la regola della catena. Tale metodo è estensivamente usato in differenti applicazioni, ad esempio per il calcolo della retropropagazione dell'errore nell'allenamento delle reti neurali artificiali, ampiamente utilizzato in applicazioni di apprendimento automatico e apprendimento profondo.mento automatico e apprendimento profondo.
, Seppo Ilmari Linnainmaa (born 28 September … Seppo Ilmari Linnainmaa (born 28 September 1945) is a Finnish mathematician and computer scientist. He was born in Pori. In 1974 he obtained the first doctorate ever awarded in computer science at the University of Helsinki. In 1976, he became Assistant Professor. From 1984 to 1985 he was Visiting Professor at the University of Maryland, USA. From 1986 to 1989 he was Chairman of the Finnish Artificial Intelligence Society. From 1989 to 2007, he was Research Professor at the VTT Technical Research Centre of Finland. He retired in 2007. Explicit, efficient error backpropagation in arbitrary, discrete, possibly sparsely connected, neural networks-like networks was first described in a 1970 master's thesis (Linnainmaa, 1970, 1976), albeit without reference to NNs, when Linnainmaa introduced the reverse mode of automatic differentiation (AD), in order to efficiently compute the derivative of a differentiable composite function that can be represented as a graph, by recursively applying the chain rule to the building blocks of the function. Linnainmaa published it first, following Gerardi Ostrowski who had used it in the context of certain process models in chemical engineering some five years earlier, but didn't publish. With faster computers emerging, the method has become heavily used in numerous applications. For example, backpropagation of errors in multi-layer perceptrons, a technique used in machine learning, is a special case of reverse mode AD.ing, is a special case of reverse mode AD.
, Seppo Linnainmaa (nacido en 1945) es un ma … Seppo Linnainmaa (nacido en 1945) es un matemático e informático finlandés. Nació en Pori. En 1974 obtuvo el primer doctorado en informática en la Universidad de Helsinki y en 1976 se convirtió en profesor adjunto. De 1984 a 1985 fue profesor Visitante en la Universidad de Maryland, Estados Unidos. Entre 1986 y 1989 fue Presidente de la Sociedad Finlandesa de Inteligencia Artificial. De 1989 a 2007 fue profesor de investigación en el Centro de Investigación Técnica de Finlandia. Se jubiló en 2007. En 1970, Linnainmaa introdujo el modo inverso de diferenciación automática (AD), para calcular eficientemente la derivada de una función compuesta diferenciable que puede representarse como un gráfico, aplicando recursivamente la regla de la cadena a los bloques de construcción de la función. Por ejemplo, la retropropagación de errores en percepciones multicapa, una técnica utilizada en el aprendizaje automático, es un caso especial del modo inverso ADo, es un caso especial del modo inverso AD
, Seppo Ilmari Linnainmaa (* 28. September 1 … Seppo Ilmari Linnainmaa (* 28. September 1945 in Pori, Finnland) ist ein finnischer Mathematiker und Informatiker. Im Jahre 1974 erlangte er die erste jemals von der Universität Helsinki vergebene Informatik-Doktorwürde. 1976 wurde er Assistenzprofessor. Von 1984 bis 1985 war er Gastprofessor an der Universität von Maryland, USA. Von 1986 bis 1989 war er Vorsitzender der Finnischen Gesellschaft für Künstliche Intelligenz. In den Jahren von 1989 bis 2007 war er Forschungsprofessor am Finnischen Technischen Forschungszentrum. Er wurde 2007 emeritiert. Im Jahre 1970 publizierte Linnainmaa den „Rückwärtsmodus“ der automatischen Differenzierung (AD) zur effizienten Berechnung der Ableitung einer differenzierbaren zusammengesetzten Funktion, die sich als Graph oder Netzwerk darstellen lässt. Der zentrale Trick besteht in der rekursiven Anwendung der Kettenregel auf die Bestandteile der Funktion. Diese Methode wird nun in zahlreichen Anwendungen verwendet. Insbesondere ist Backpropagation von Fehlern in künstlichen neuronalen Netzen ein Spezialfall von Linnainmaa's Verfahren.in Spezialfall von Linnainmaa's Verfahren.
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Seppo Linnainmaa (Pori (Finlandia), 1945) … Seppo Linnainmaa (Pori (Finlandia), 1945) è un matematico e informatico finlandese.Nel 1974 fu il primo a ricevere un dottorato in informatica dall'Università di Helsinki, e nel 1976 divenne assistant professor. Dal 1984 al 1985 fu visiting professor all'Università del Maryland e dal 1986 al 1989 fu presidente della Finnish Artificial Intelligence Society. Dal 1989 al 2007, anno del suo pensionameto, fu professore di ricerca al Technical Research Centre of Finland.a al Technical Research Centre of Finland.
, Seppo Ilmari Linnainmaa (born 28 September … Seppo Ilmari Linnainmaa (born 28 September 1945) is a Finnish mathematician and computer scientist. He was born in Pori. In 1974 he obtained the first doctorate ever awarded in computer science at the University of Helsinki. In 1976, he became Assistant Professor. From 1984 to 1985 he was Visiting Professor at the University of Maryland, USA. From 1986 to 1989 he was Chairman of the Finnish Artificial Intelligence Society. From 1989 to 2007, he was Research Professor at the VTT Technical Research Centre of Finland. He retired in 2007.rch Centre of Finland. He retired in 2007.
, Seppo Linnainmaa (nacido en 1945) es un ma … Seppo Linnainmaa (nacido en 1945) es un matemático e informático finlandés. Nació en Pori. En 1974 obtuvo el primer doctorado en informática en la Universidad de Helsinki y en 1976 se convirtió en profesor adjunto. De 1984 a 1985 fue profesor Visitante en la Universidad de Maryland, Estados Unidos. Entre 1986 y 1989 fue Presidente de la Sociedad Finlandesa de Inteligencia Artificial. De 1989 a 2007 fue profesor de investigación en el Centro de Investigación Técnica de Finlandia. Se jubiló en 2007.n Técnica de Finlandia. Se jubiló en 2007.
, Seppo Ilmari Linnainmaa (* 28. September 1 … Seppo Ilmari Linnainmaa (* 28. September 1945 in Pori, Finnland) ist ein finnischer Mathematiker und Informatiker. Im Jahre 1974 erlangte er die erste jemals von der Universität Helsinki vergebene Informatik-Doktorwürde. 1976 wurde er Assistenzprofessor. Von 1984 bis 1985 war er Gastprofessor an der Universität von Maryland, USA. Von 1986 bis 1989 war er Vorsitzender der Finnischen Gesellschaft für Künstliche Intelligenz. In den Jahren von 1989 bis 2007 war er Forschungsprofessor am Finnischen Technischen Forschungszentrum. Er wurde 2007 emeritiert.rschungszentrum. Er wurde 2007 emeritiert.
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Seppo Linnainmaa
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